A basic result in LOCC theory [1]}, [2]}, [3]} shows that any set of orthogonal product states in \(\mathbb {C}^{2} \otimes \mathbb {C}^{d}\)  for arbitrary \(d\ge 2\)  can be distinguished via full (two-way) LOCC. This is readily seen to not be the case for one-way LOCC. As a simple example, consider the two-qubit set \(\lbrace | 00 \rangle ,| 10 \rangle , | +1 \rangle , | -1 \rangle \rbrace \)  where \(| + \rangle =\frac{1}{\sqrt{2}}(| 0 \rangle +| 1 \rangle )\)  and \(| - \rangle =\frac{1}{\sqrt{2}}(| 0 \rangle -| 1 \rangle )\) . This set of four two-qubit states cannot be distinguished by one-way LOCC with Alice going first; they can however be distinguished by one-way LOCC with Bob going first and hence also by two-way LOCC.
